Replace the letter A in the integral Aeºr³-31² 1 da so that the integral evaluates to 023 32² + C.

Q: Verify whether the following equations are exact. If possible, solve the equation. y a) dx- - 2 X +²…

A: (a) xx2-y2dx-yx2-y2dy=0(b) 2x+6x2ydx+3y2+2x3dy=0

Q: The curve represented by the equation  r = aeb?,  where a and b are constants, is called a…

A: r=e?/6 ; -2≤ ? ≤ 2let ? be xhere x is dummy variable.so,r=ex6; -2≤x≤2

Q: 1. The function S(t) (where t is measured in weeks starting with t = 0) approximates the stock…

A: Numerical integration

Q: In the triangle below Ĉ= 90°, AC = 2 and BC = 4 B cosec (B) = C A Q

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Q: A function is continuous and twice differentiable for all z 1. Its derivatives have the properties…

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Q: Let r(t) = (2t³-3, 2e-t, 3 sin(-2t)) Find the unit tangent vector T(t) at the point t = 0 T(0) =…

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Q: Find the first partial derivatives of the function. f(x, y, z) = x³yz² + 7yz 2.2 f(x, y, z)= 3x y=²…

A: f(x, y, z) = x3 y z2 + 7 yz Find the first partial derivative of the function

Q: se the Laplace transform to solve the given initial-value problem.   1. y' − y = 2 cos(2t),  y(0) =…

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: The graph of f is shown in the figure. 6 -2 f 24 6

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Q: The curves F1(t)= (-2t, t, 4t) and 2(t) = (sin(3t), sin(4t), t - 7) intersect at the origin. Find…

A: NOTE: Refresh your page if you can't see any equations. . both curves intersect at the origin…

Q: Find the length of the curve x(t) = e²t cos(t), y = e2t sin(t) for 0 ≤ t ≤ 4. Give an exact answer,…

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Q: A company makes three sizes of cardboard boxes: small, medium, and large. It costs $1.50 to make a…

A: Number of small boxes=xNumber of medim boxes=yNumber of large boxes=z

Q: 7.. State the first five partial sums of " mln+1 Show complete work.

A: Given that ∑n=1∞nn+1We have to find first five partial sum

Q: 1. Evaluate: f (2x+3)dx x²+2x+5

A: As per our guild line we are supposed to answer only one question please repost other questions as…

Q: Volume. Apply the Cylindrical Shell method to find the volume of the solid obtained by rotating the…

A: We are given two curves and rotating the bounded region about y-axis.

Q: Use the chain rule to find дz əs дz at || Z= sin(0) r дz əs and дz at r = st, 0 = s5 +t5

A: we have given z=sinθr, r=st and θ=s5+t5 we need to find the given partial derivatives

Q: the following steps for the given function, interval, and value of n. a. Sketch the graph of the…

A: Option C

Q: (2) Σε i=5 ¹(¹7) = sin (b) Σκίτ (c) 24 = J=0 =

A: We have to evaluate each of the summation notation

Q: The population of a town is increasing at a rate given by P'(t) = 45e0.016t where P is the…

A: given P'(t)=45e0.016t where t is population t years after the beginning of 1990 given population at…

Q: Evaluate the limits u DR in words): ΔΔΔ Tim DX-40+ [(tan 2x)^ ] = 7.

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Q: the same cardinality. Show that the set of all even integers and the set of all odd integers have

A: To prove that two sets have same or equal cardinality it is enough to prove that there is exist a…

Q: Suppose z = x² sin y, x = -4s² + t², y = -2st. A. Use the chain rule to find and Əs Ət = as…

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Q: Find parametric equations for the tangent line to the curve r(t) = (t² +e²t)i + (2+e¯³)j + (t³ −…

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Q: 2 S.S.x'y dydx x²y³ 0 0

A: ∫01∫02x2y3dydx

Q: Find all the critical points of f(x) = x(5-x) 4. 1. x = 5, 1

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Q: A graphing calculator is recommended. Suppose that the rabbit population on Mr. Jenkins' farm…

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Q: The expression (3/1/5) 3/5 equals y where r, the exponent of y, is:

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Q: Evaluate. (Be sure to check by differentiating!) 1 9 Jes dx, x# -- 5 1 dx= 9+5x (Type an exact…

A: Here we evaluate the given integral and Check by differentiating.

Q: Inx Find the limit. Apply L'Hop rule. lim- X-00

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Q: which of following is graph of F(x) = Xº Dashed 4²-1 lines indicate asymplates

A: To find the vertical asymptote: Set denominator=0 and solve for x. To find the horizontal asymptote:…

Q: Calculate the volume of the solid obtained if the plane region R bounded by y=x and x= 4y - y2 is…

A: y=x and x=4y-y2

Q: 3 1 1 Use the transformation u = 3x+4y, v=x+3y to evaluate the given integral for the region R…

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Q: Problem 10. Consider the following first order differential equation. Check that it is separable.…

A: The given equation is:(e-5x+y+ey)y'=5

Q: Use an appropriate change of variables to evaluate the integral 1. I = when D is the region in the…

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Q: Use the appropriate ²¹e²+0.5z te a. ₂2x methods to solve the following integrals. dx

A: According to question,Given Integral,∫01ex+e0.5xe2x dx

Q: Find the associated half-life time or doubling time. (Round your answer to three significant…

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Q: 5T Convert the point (r, 0, z)=(5, expressions, or decimals to at least one decimal place. (x, y, z)…

A: Given: We will be converting the above to a cartesian coordinate. So,          x=r cosθ=5…

Q: Find the critical numbers of the function. (Enter your answers as a comma-separated list. If an…

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Q: Find the exact area of the region bounded by the curves y = 10x² - 6x + 14 and y=9x - 4x+14. Answer…

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Q: 2 a) Find the points on the curve y=x²-6x² +4 where the tangent line is horizontal.

A: Note :- Since you have posted multiple questions, we will provide the solution only to the first…

Q: 1, Compute the Euclidean distance between the sets of points below. a. ​(2​,4​)and ​(9​,3​) b.…

A: a) two point in 2 dimension is (2, 4) and (9, 3)  b) two point in 3 dimension is (11, -3, 30) and…

Q: Convert the point (x, y, z) positive values, either as expressions, (r, 0, z) = 1C Calculator Check…

A: We compare xy and r-theta plane

Q: Given the tangent to y = lnx is y = its equation. at (e, 1). Find a parallel tangent to y = e* and…

A: Given that the tangent to y = lnx is y=(1/2)x at (e,1).  Here we have to find a parallel tangent to…

Q: 4 Find f such that f'(x) = - f(x) = 0 √√x f(16) = 44.

A: Given,            f'x=4x , f16=44

Q: Given the vector function r(t) = (-t, - 2t³, 5t5 + 1) Find the velocity and acceleration vectors at…

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Q: In the article "Do Dogs Know Calculus?" the author Timothy Pennings explained how he noticed that…

A: Let DC be x and t(x) represents the time taken by the dog, Elvis in travelling the distance AD at a…

Q: Find the directional derivative of f at the given point in the direction indicated by the angle 8. π…

A: The given function is fx,y=ycosxy. Evaluate the gradient of the function at the given point.…

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) 6x - 2y lim (x,y) → (2, 6)…

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Q: Let f(x) = x²-7X, 9(x) = sin(x) and P(x) = { *³²³²^(x), *²0 x=0 a) use the limit definition of the…

A: We need to find derivative of given function.

Q: Find the local linear approximation of the function f(x)=√1+zat zo = 3, and use it to approximate…

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